When organic search results aren't enough, you might eventually end up advertising on Google. Their regular ad platform is called AdWords.
But Search Engine Optimization isn't only about advertising. Actually, it starts with your development practices which truly optimize performance, accessibility, and platform responsiveness of your website. See the resources provided by Google on the subject: https://developers.google.com/web/fundamentals/performance/
Google has a new tool called Keyword Planner that replaces their former "Google Keyword Tool" 
A service that I just learned about is Majestic. As they put it:
Find out how all the websites on the internet link to each other with the largest Link Intelligence database on the planet. No other site or search engine gives you as much detailed information about how the fabric of the web is knitted together.
Majestic is interesting, and has an API as well if you need to integrate their data into your application.